Commitment and matching in the marriage market

The set of stable marriage matches is different depending on whether allocation within marriage is determined by binding agreements in the marriage market (BAMM) or by bargaining in marriage (BIM). With transferable utility, any stable matching is utilitarian efficient under BAMM, but not under BIM. Is it possible to implement the efficient matching under BIM? We show that if one side of the market is sufficiently sensitive relative to the other, if the more sensitive side can be ranked by sensitivity, and if their preferences are hierarchical, the top trading cycles algorithm results in an efficient matching.